We already emphasized (see Figure REF ) the importance of VBF for the direct production of new physics particles. The relevance of VBF for probing new physics indirectly simply stems for the huge rate of VBF SM processes, summarized on the right panel of Figure REF . In particular we see that a 10 TeV muon collider produces ten million Higgs bosons, which is around 10 times more than future \(e^+e^-\)  Higgs factories. Since the Higgs bosons are produced in a relatively clean environment, a 10 TeV muon collider (over-)qualifies as a Higgs factory [1]}, [2]}, [3]}, [4]}, [5]}. Unlike \(e^+e^-\)  Higgs factories, a muon collider also produces Higgs pairs copiously, enabling accurate measurements of the Higgs trilinear coupling [6]}, [3]}, [8]} and possibly also of the quadrilinear coupling [9]}.
